# Factors, Multiples and Primes

## Multiples

The multiples of a number are all the numbers in its times table.
The multiples of 5 are all the numbers in the 5 times table.

Example 1:
Write down the first 5 multiples of 3

We need to write down the first 5 numbers in the 3 times table.
1 × 3 = 3
2 × 3 = 6
3 × 3 = 9
4 × 3 = 12
5 × 3 = 15

The first 5 multiples of 3 are 3, 6, 9, 12 and 15.

Example 2:
Write down the first 5 multiples of 5

We need to write down the first 5 numbers in the 5 times table.
1 × 5 = 5
2 × 5 = 10
3 × 5 = 15
4 × 5 = 20
5 × 5 = 25

The first 5 multiples of 5 are 5, 10, 15, 20 and 25.

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## Factors

The factors of a number are the numbers that multiply together to make it.
The factors of 10 are the numbers that you can multiply together to make 10. 2 × 5 = 10, so 2 and 5 are both factors of 10 (so are 1 and 10).

Example 1:
Write down all the factors of 20

1 × 20 = 20
Next we can try 2: 2 × 10 = 20
20 is not in the 3 times table, so 3 is not a factor.
4 × 5 = 20
We don't need to check any other numbers because we would only get repeats of the ones we already have.

The factors of 20 are: 1, 2, 4, 5, 10 and 20.

Example 2:
Write down all the factors of 16

We will check in order again:
1 × 16 = 16
2 × 8 = 16
16 is not in the 3 times table
4 × 4 = 16 (16 is a square number)
We don't need to check any other numbers because we would only get repeats of the ones we already have.

The factors of 16 are: 1, 2, 4, 8 and 16.

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## Prime Numbers

A prime number is a number with exactly 2 factors.
5 is a prime number because its only factors are 1 and 5.
6 is not a prime number because its factors are 1, 2, 3 and 6.

Example 1:
Write down all prime numbers between 1 and 10.

1 is not a prime number because it only has one factor. It is only 1 × 1.
2 is a prime number - its only factors are 1 and 2.
3 is a prime number - its only factors are 1 and 3.
4 is not a prime number: it is in the 2 times table (so 2 is a factor as well as 1 and 4).
5 is a prime number - its only factors are 1 and 5.
6 is not a prime number: it is in the 2 (and 3) times table.
7 is a prime number.
8 is not a prime number: it is in the 2 (and 4) times table.
9 is not a prime number: it is in the 3 times table.
10 is not a prime number: it is in the 2 (and 5) times table.

The prime numbers between 1 and 10 are 2, 3, 5 and 7.

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